Moving Crystal Phases of a Quantum Wigner Solid in an Ultra-High-Quality 2D Electron System

In low-disorder, two-dimensional electron systems (2DESs), the fractional quantum Hall states at very small Landau level fillings ($\nu$) terminate in a Wigner solid (WS) phase, where electrons arrange themselves in a periodic array. The WS is typically pinned by the residual disorder sites and manifests an insulating behavior, with nonlinear current-voltage ($I\text{−}V$) and noise characteristics. We report here measurements on an ultralow-disorder, dilute 2DES, confined to a GaAs quantum well. In the $\nu <1/5$ range, superimposed on a highly insulating longitudinal resistance, the 2DES exhibits a developing fractional quantum Hall state at $\nu =1/7$, attesting to its exceptional high quality and dominance of electron-electron interaction in the low filling regime. In the nearby insulating phases, we observe remarkable nonlinear $I\text{−}V$ and noise characteristics as a function of increasing current, with current thresholds delineating three distinct phases of the WS: a pinned phase (P1) with very small noise, a second phase (P2) in which $dV/dI$ fluctuates between positive and negative values and is accompanied by very high noise, and a third phase (P3) where $dV/dI$ is nearly constant and small, and noise is about an order of magnitude lower than in P2. In the depinned (P2 and P3) phases, the noise spectrum also reveals well-defined peaks at frequencies that vary linearly with the applied current, suggestive of washboard frequencies. We discuss the data in light of a recent theory that proposes different dynamic phases for a driven WS.

Figure 1

Longitudinal resistance ($R_{xx}$) vs magnetic field ($B$) for a dilute 2DES confined to an 89-nm-wide GaAs quantum well at $T\simeq 72\mathrm{mK}$ in the small filling range. The position of an emerging FQHS at $\nu =1/7$ is marked. Inset: $R_{xx}$ at $T\simeq 30\mathrm{mK}$ in the higher filling range.

Figure 2

(a) $dV/dI$ vs $I$ at $B=8.40\mathrm{T}$ ($\nu =0.139$). The different traces, corresponding to different temperatures $T\simeq 80$, 85, 90, and 96 mK, are offset vertically by 12, 8, 4, and $0\mathrm{M}\mathrm{\Omega }$, respectively. (b) Color-scale plot summarizing $dV/dI$ vs $I$ curves for all temperatures. The dashed white line follows the first minimum corresponding to the negative differential resistance seen just beyond $I_{\mathrm{th}1}$. (c) The integrated $I\text{−}V$ characteristics at different temperatures.

Figure 3

Noise data at $B=7.50\mathrm{T}$ ($\nu =0.155$). (a),(b) $dV/dI$ (blue trace) and noise power obtained by averaging over a frequency window of $\pm 10\mathrm{Hz}$ centered at 40 Hz defined as $S_{40}$ (red trace) vs $I$ at $T\simeq 61$ and $\simeq 78\mathrm{mK}$, respectively. (c) $S_{40}$ vs $I$ at different temperatures. The scale for $S_{40}$ is logarithmic and spans over four decades. (d),(e) Color-scale plots summarizing the noise power as a function of $f$ and $I$ at $T\simeq 61$ and $\simeq 78\mathrm{mK}$, respectively. (f),(g) Noise power vs $f$ for different values of $I$ as indicated.

Figure 4

Phase diagram for the WS as a function of $T$ and $I$ at $B=7.50\mathrm{T}$ ($\nu =0.155$).